**Addition and Subtraction Rational Expressions Worksheet :**

Here we are going to see some practice questions on adding and subtracting two rational expressions.

Like adding and subtracting two rational numbers, we have two methods to add or subtract two rational expressions.

**Addition and Subtraction of Rational Expressions with Like Denominators :**

(i) Add or Subtract the numerators

(ii) Write the sum or difference of the numerators found in step (i) over the common denominator.

(iii) Reduce the resulting rational expression into its lowest form

**Addition and Subtraction of Rational Expressions with unlike Denominators :**

(i) Determine the Least Common Multiple of the denominator.

(ii) Rewrite each fraction as an equivalent fraction with the LCM obtained in step (i). This is done by multiplying both the numerators and denominator of each expression by any factors needed to obtain the LCM.

(iii) Follow the same steps given for doing addition or subtraction of the rational expression with like denominators.

(1) Simplify

(i) [x (x + 1)/(x - 2)] + [x(1 - x)/(x - 2)] Solution

(ii) (x + 2)/(x + 3) + (x - 1)/(x - 2) Solution

(iii) [x^{3}/(x - y)] + [y^{3}/(y - x)] Solution

(2) Simplify

(i) [(2x + 1)(x - 2)/(x - 4)] - [(2x^{2} - 5x + 2)/(x - 4)]

(ii) 4x/(x^{2} - 1) - (x + 1)/(x - 1) Solution

(3) Subtract 1/(x^{2} + 2) from (2x^{3} + x^{2} + 3)/(x^{2} + 2)^{2}

(4) Which rational expression should be subtracted from

(x^{2} + 6x + 8)/(x^{3} + 8) to get 3/(x^{2} - 2x + 4)

(5) If A = (2x + 1)/(2x - 1) and B = (2x - 1)/(2x + 1) find 1/(A - B) - 2B/(A^{2} - B^{2}) Solution

(6) If A = x/(x + 1), B = 1/(x + 1), prove that

((A + B)^{2} + (A- B)^{2})/(A ÷ B) = 2(x^{2} + 1)/x(x + 1)^{2}

(7) Pari needs 4 hours to complete a work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together? Solution

(8) Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ₹ 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy? Solution

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